Ocean waves can travel in any direction, but waves breaking on the sea-shore are usually approximately parallel to the line of the beach. How can Huygens' principle explain this phenomenon? Does it have something to do with the fact that the velocity of the waves decreases as the water gets shallower?
[Physics] Huygens’ Principle and Ocean Waves
huygens-principlewaves
Best Answer
Yes. In deep water the speed of an ocean wave is approximately independent of the depth. But in shallow water (a working definition is the depth is much smaller than the wavelength), the wave speed is proportional to the square root of the depth (see for example What determines the speed of waves in water? ).
You can then extend this to an optics analogy (and Huygens principle) by noting that as the wave speed decreases towards the shore (shallower depth), that is equivalent to increasing the refractive index of the water. So you can imagine the wave propagating at some angle to the shore being "refracted" such that its propagation direction is diverted towards being more towards perpendicular to the shoreline (or at least towards where the gradient of depth is largest).
To use Huygen's principle in this case, you could divide the water up into strips, parallel to the shore, each with its own refractive index (increasing towards the shore). Then apply the usual Huygen's wavelet construction that is used to prove Snell's law at each interface between two media with different refractive indices.